1. Milankovich cycle (Astronomical cycle) are importent in the long term beyond centuaries

2. The solar constant variation is less than 0.1% definitely in the last 25 years, probably in the last century and possibly in the last million years.

3. Green house gases have experienced long term natural and recent anthropogenic changes. The warming effect of green house gases and cooling effect of sulphite aerosols explains the recent warming trend.

4. Deep Ocean Circulation changes can cause climate changes which require mere decades to significantly alter land and sea surface temperature. This has occurred in relatively recent past of about 10000 years ago and may be possible if triggered by greenhouse warming.

5. The coupled ocean atmosphere system oscillates and produce inter annual and decadal variations in climate, which are predictable in some extend

6. Cloud radiation interaction is another important factor which have strong influence on climate. But no past data is available for the pre satellite era.

7. Land surface changes also have influence on climate but most of them are local and irreversible. One of the major example is the influence of Himalayas orography and Asian monsoon

2. The Ekman transport converges at the subtropics causes downwelling. The diverging region of Ekman transport cause upwelling.(Reason: Continuity and conservation of mass)

3. The downwelling push the thermocline down and squeeze the underling geostrophic layer. The upwelling pull the thermocline up and stretches the geostrophic layer.(Reason: Continuity and conservation of mass)

where is the density of the diffusing material at location and time t and is the collective diffusion coefficient for density φ at location ; the nabla symbol represents the vector differential operatordel acting on the space coordinates. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear. If is constant, then the equation reduces to the following linear equation:

also called the heat equation. More generally, when D is a symmetric positive definite matrix, the equation describes anisotropic diffusion, which is written (for three dimensional diffusion) as:

Derivation

The diffusion equation can be derived in a straightforward way from the continuity equation, which states that a change in density in any part of the system is due to inflow and outflow of material into and out of that part of the system. Effectively, no material is created or destroyed:

,

where is the flux of the diffusing material. The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which assumes that the flux of the diffusing material in any part of the system is proportional to the local density gradient:

.

Historical origin

Discrete analogs

The diffusion equation is continuous in both time and space. One may discretize space, time, or both space and time, which arise in application. Discretizing time alone just corresponds to taking time slices of the continuous system, and no new phenomena arise. In discretizing space alone, the Green's function becomes the discrete Gaussian kernel, rather than the continuous Gaussian kernel. In discretizing both time and space, one obtains the random walk.